Quadratic Function

From GM-RKB
(Redirected from quadratic function)
Jump to navigation Jump to search

A Quadratic Function is a polynomial function with a function degree of two.



References

2015

  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/quadratic_function Retrieved:2015-11-7.
    • In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree. For example, a quadratic function in three variables x, y, and z contains exclusively terms x2, y2, z2, xy, xz, yz, x, y, z, and a constant: : [math]\displaystyle{ f(x,y,z)=ax^2+by^2+cz^2+dxy+exz+fyz+gx+hy+iz +j, }[/math] with at least one of the coefficients a, b, c, d, e, or f of the second-degree terms being non-zero.

      A univariate (single-variable) quadratic function has the form : [math]\displaystyle{ f(x)=ax^2+bx+c,\quad a \ne 0 }[/math] in the single variable x. The graph of a univariate quadratic function is a parabola whose axis of symmetry is parallel to the y-axis, as shown at right.

      If the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the univariate equation are called the roots of the univariate function.

      The bivariate case in terms of variables x and y has the form : [math]\displaystyle{ f(x,y) = a x^2 + by^2 + cx y+ d x+ ey + f \,\! }[/math] with at least one of a, b, c not equal to zero, and an equation setting this function equal to zero gives rise to a conic section (a circle or other ellipse, a parabola, or a hyperbola).

      In general there can be an arbitrarily large number of variables, in which case the resulting surface is called a quadric, but the highest degree term must be of degree 2, such as x2, xy, yz, etc.